Soil moisture retrieval over agricultural fields from multi-polarized and multi-angular RADARSAT-2 SAR data

Remote Sensing of Environment 115 (2011) 33–43

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Remote Sensing of Environment j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / r s e

Soil moisture retrieval over agricultural fields from multi-polarized and multi-angular RADARSAT-2 SAR data Imen Gherboudj a,⁎, Ramata Magagi a, Aaron A. Berg b, Brenda Toth c a b c

Université de Sherbrooke, Centre d'applications et de recherches en télédétection (CARTEL), 2500 Boulevard de l'Université, J1K 2R1, Sherbrooke, QC, Canada University of Guelph, Department of Geography, 50 Stone road East, N1G 2W1, Guelph, Ontario, Canada Environment Canada, MSC Hydrometeorology and Arctic Lab, 11 Innovation boulevard, S7N 3H5, Saskatoon, SK Canada

a r t i c l e

i n f o

Article history: Received 22 January 2010 Received in revised form 28 July 2010 Accepted 29 July 2010 Keywords: RADARSAT-2 Polarization ratios Modelling Empirical relationships Ground measurements Agricultural fields Crop height Crop water content Soil surface roughness Soil moisture

a b s t r a c t The aim of this study was to estimate soil moisture from RADARSAT-2 Synthetic Aperture Radar (SAR) images acquired over agricultural fields. The adopted approach is based on the combination of semi-empirical backscattering models, four RADARSAT-2 images and coincident ground measurements (soil moisture, soil surface roughness and vegetation characteristics) obtained near Saskatoon, Saskatchewan, Canada during the summer of 2008. The depolarization ratio (χv), the co-polarized correlation coefficient (ρvvhh) and the ratio of the absolute value of cross polarization to crop height (Λvh) derived from RADARSAT-2 data were analyzed with respect to changes in soil surface roughness, crop height, soil moisture and vegetation water content. This sensitivity analysis allowed us to develop empirical relationships for soil surface roughness, crop height and crop water content estimation regardless of crop type. The latter were then used to correct the semi-empirical Water–Cloud model for soil surface roughness and vegetation effects in order to retrieve soil moisture data. The soil moisture retrieved algorithm is evaluated over mature crop fields (wheat, pea, lentil, and canola) using ground measurements. Results show average relative errors of 19%, 10%, 25.5% and 32% respectively for the retrieval of crop height, soil surface roughness, crop water content and soil moisture. © 2010 Elsevier Inc. All rights reserved.

1. Introduction Radar remote sensing has important implications in agricultural monitoring, in particular for crop growth, yield and mapping as well as for soil moisture estimation, which is a major challenge in the presence of vegetation cover (De Roo et al., 2001; Della Vecchia et al., 2008; Lin et al., 2009; McNairn et al., 2009; Satalino and Mattia, 2009). The objective of the present study is to investigate the potential of RADARSAT-2 linear polarization data for soil moisture estimation over agricultural fields. Efforts by several authors to use radar data to estimate soil moisture over such areas have encountered some limitations due to low temporal frequency of data acquisition, noise associated with vegetation cover, soil surface roughness and to some extent soil texture (Fung and Eom, 1985; Ulaby et al., 1986).

⁎ Corresponding author. Tel.: + 1 819 821 8000x63261; fax: + 1 819 821 7944. E-mail addresses: [email protected] (I. Gherboudj), [email protected] (R. Magagi), [email protected] (A.A. Berg), [email protected] (B. Toth). 0034-4257/$ – see front matter © 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2010.07.011

For soil moisture estimation, low frequency L-band (24 cm wavelength) is more suitable than high frequency X-band (3 cm wavelength) which less penetrates the vegetation volume (Fung, 1994; Ulaby et al., 1986). At an intermediate frequency such as the Cband (6 cm wavelength) used in this study, the signal is reflected from both the canopy and the soil surface. The predominant component between the soil and the vegetation is highly dependent on soil and vegetation characteristics as well as on the sensor incidence angle and polarization. At high incidence angle, the soil contribution is reduced to the benefit of vegetation contribution, leading therefore to less sensitivity to soil parameters and in particular soil moisture. However, using C-band multi-polarization and multi-angular SAR data acquired under high biomass conditions, Romshoo et al. (2002) showed an appreciable sensitivity to soil moisture even if the sensitivity to vegetation water content is high. Broad-leafed crops (corn, soybean, etc.) signal saturates early at C- and L-bands, while the grain crops (wheat, oat, rice, etc.) allow a very dynamic temporal variation resulting from the changes in both soil and vegetation (SoriaRuiz et al., 2009). Depending on the crop structure, the polarization affects the signal's sensitivity to soil moisture. In general, at high incidence angle, the loss factor of vegetation in horizontal polarization is lower than in vertical polarization. Considering these information, over mature crops, the signal acquired in C-band and in only one

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measurement configuration (polarization or incidence angle) is not sufficient to estimate soil moisture. Nevertheless, the accuracy in soil moisture estimation can be enhanced from the sensors currently in orbit (RADARSAT-2, ASAR/ENVISAT, TerraSAR-X, and ALOS/PALSAR). They provide multi-configuration (multi-temporal, multifrequency, multi-angular, and multi-polarization) radar data that make it possible to address soil moisture estimation and monitoring issues in more effective ways (Baghdadi et al., 2009). Methods use either backscattering model-based retrieval algorithms (Bindlish and Barros, 2001; Joseph et al., 2009) or polarimetric information derived from target decomposition techniques (Cloude and Pottier, 1996; Hajnsek et al., 2009; Jagdhuber et al., 2009). In the former case, the semi-empirical Water–Cloud model (Attema and Ulaby, 1978), appreciated for its simplicity, is used widely in both direct and inverse modeling of the scattering of vegetated areas (Bindlish et al., 2001; Prevot et al., 1993). For an optimal inversion process of soil moisture estimation over agricultural fields, assumptions (e.g. invariant soil surface roughness or crop height) are generally made to reduce the number of unknown parameters. Recently, using polarimetric L-band airborne data acquired over agricultural areas, Jagdhuber et al. (2009) showed that a significant improvement in soil moisture estimation could be obtained by increasing multi-angular acquisitions. The inversion rate thus increased from 30–49% for a single angular acquisition to over 55–63% and 70% respectively for two and three angular acquisitions (Jagdhuber et al., 2009). In addition, some authors have used polarization ratios to discriminate between surface parameters or to highlight or minimize the effect of certain parameters on the signal and thus improve the soil moisture retrieval algorithm (Bindlish et al., 2001; De Roo et al., 2001; Owe et al., 2001; Sikdar et al., 2005; Ulaby et al., 1986). Over bare soils, the co-polarization ratio reaches saturation for high soil surface roughness values, thus simplifying soil moisture estimation (Oh, 2004; Oh et al., 1992; Ulaby et al., 1986). Similarly, the depolarization ratio (VH to VV polarization) has been found very sensitive to soil surface roughness (Srivastava et al., 2008; Ulaby et al. 1986). However, it was sensitivity analyses of these ratios with respect to soil (roughness and moisture) and sensor (frequency, incidence angle and polarization) characteristics that led to the well-known empirical backscattering models of bare soil developed by Oh et al. (1992), Dubois et al. (1995) and Oh (2004). Over vegetated surfaces, several empirical relationships have been developed between polarization and/or dual frequency ratios and physical parameters of crop fields. For example, the radar vegetation index (RVI) computed at L-band has been used to evaluate the biomass level of a corn crop (Yunjin and Van Zyl, 2009). Good correlations between HV/VV and soybean water content have been obtained in L-band (De Roo et al., 2001), between VV/HV and maize crop height and biomass at S- and C-bands (Della Vecchia et al., 2008). The HV/HH ratio at C-band has been used to estimate the leaf area index (LAI) of sugarcane (Lin et al., 2009). While these cross polarization ratios are almost insensitive to soil moisture, it must not be overlooked that the above-mentioned relationships were developed for specific crops. In this paper, the relationship between VH/VV to crop height is analysed with respect to changes in both the root mean square height of soil surface roughness and incidence angle, regardless of crop type. Simulations were performed to support experimental results and to highlight soil surface roughness and incidence angle effects on VH/VV. In contrast with previous studies, in which HV/VV was related to vegetation parameters (water content, height, biomass), this ratio is used in the present study to assess the rms height of soil surface roughness. In addition, based on ground measurements and on RADARSAT-2 multipolarization information, new relationships were developed to estimate crop height and water content. Using estimates of soil surface roughness and vegetation parameters, soil moisture is retrieved from the inversion of the Water–Cloud model (Attema and Ulaby, 1978).

2. Scattering models Over bare soil surfaces characterized by random roughness, the 0 backscattering coefficient (σpqs ) can be expressed using the semiempirical model of Oh (2004) given by h
i 0 σhvs = 0:11Ms0:7 ðcosθÞ2:2 1− exp −0:32ðksÞ1:8 0 n h io σhvs 1:4 0:9 = 0:095ð0:13 + sinð1:5θÞÞ 1− exp −1:3ðksÞ 0 σvvs   −0:65
 σ0 θ 0:35Ms 1:4 p = hhs = 1− exp −0:4ðksÞ 0 90∘ σvvs

q=

ð1Þ

where k is the wave number, s is the rms height of soil surface roughness, Ms is soil moisture and θ is the incidence angle. The range of validity for this model is 0.04 b Ms b 0.291 m3/m3, 0.13 b ks b 6.98 and 10° b θ b 70°. In the presence of a vegetation canopy, the total backscattering 0 signal results from soil surface scattering (σsoil ), the volume scattering 0 of the vegetation elements (σvol) and the volume–surface interaction 0 term (σint ). In this paper, we account for the vegetation cover as well as the soil surface using the Water–Cloud model (Attema and Ulaby, 1978), which as a simple formulation of the first-order radiative transfer solution, neglects the multiple scattering. This model calculates backscatter based on a simplified vegetation canopy which acts as a homogeneous dielectric slab comprised of identical, uniformly distributed water particles and that its most important variables are the depth and density of the cloud, a function of water content. This simplification is acceptable for RADARSAT-2 frequency (C-band), since the signal penetration depth and therefore the multiple scattering term are low compared to that of L-band. The model is expressed as follows: 0

0

0

σpq;tot = σvol + σsoil =

 σpq1 cosθ
2 2 0 1−Tpq + Tpq σpqs 2κepq

ð2Þ

where 0 σpq, tot

total backscattering signal

0 σpq1

backscatter cross section per unit volume of the canopy (m2/m3) backscattering coefficient of soil surface pq-polarized extinction coefficient of vegetation Two-way transmissivity of the vegetation layer

0 σpqs κepq T2pq

T2pq can be expressed as follows (Kirdiashev et al., 1979): 2

−2τpq secθ

Tpq = e

ð3Þ

Vegetation layer optical depth τpq is theoretically related to crop height (h) and to the extinction coefficient of the medium (κepq) as follows: τpq = κepq h

ð4Þ

However, empirical relationships have been developed between τpq and the vegetation water content (WC, in kg per square meter) or leaf area index (LAI). According to Jackson and O'Neill (1990), τpq = bWC

ð5Þ

where b is an empirical parameter. As described by several authors (Kirdiashev et al., 1979; Jackson and Schmugge, 1991), it depends on both vegetation properties (type, shape, etc.) and sensor configuration (wavelength, polarization and look angle). Several estimations of the parameter b have been published for different frequencies,

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incidence angles and crop type (Ulaby and Wilson, 1985; Van De Griend and Wigneron, 2004; Wigneron et al., 1995). Considering Eqs. (3)–(5), Eq. (2) can be rewritten as follows: 0

σpq;tot

 A cosθ
−2bWCsecθ 0 −2bWCsecθ h 1−e + σpqs e = 2bWC

ð6Þ

0 In Eq. (6), the soil backscattering coefficient σpqs is computed using the semi-empirical Oh model expressed by Eq. (1). The A parameter represents the vegetation scattering (σpq1). Its accurate estimation requires a sufficient knowledge of vegetation canopy in terms of water content, height, structure, scatterer's size and orientation, etc. Such information is not wholly available over the studied fields. Therefore, to determine A and b parameters for a given crop type, the Water–Cloud model (Eq. (6)) was fitted against experimental data measured over few fields. The parameters A and b are thus assumed constant for each crop type in the same phenological stage. Section 4.2 describes the estimation of A and b parameters, a necessary step prior the inversion of soil moisture presented in Section 4.3.

3. Study area and measurements The study area is a relatively flat agricultural region located south of Saskatoon (Longitude: 106° 27′W, Latitude: 51° 21′N), Saskatchewan, Canada (Fig. 1). Over this area, 16 fields with a large variety of crops (wheat, lentils, peas, fallow, canola and pasture) were selected to conduct ground measurements of soil and vegetation characteristics between July 19 and July 24, 2008. The variety of crops, together with the size of the fields (reaching 60 ha, i.e. several orders of magnitude greater than the spatial resolution of the sensors used), make this area very suitable for testing the soil and vegetation parameter monitoring capabilities of SAR remote sensing. 3.1. Synthetic aperture radar (SAR) measurements During the field campaign (July 19–24, 2008), four RADARSAT-2 SAR images acquired over the study area were provided by the Canadian Space Agency through the SOAR (Science and Operational Applications Research) program. They were calibrated and then georeferenced. In this study, we focused only on the linear polarizations HH, VV and HV. For each polarization image, the mean backscattering coefficients and incidence angles of the 16 selected fields mentioned above were extracted using PCI Geomatics Software, version 10.1.3 (www.pcigeomatics.com). Table 1 presents the main specifications of these images, which show differences in data acquisition (incidence angle and polarization).

35

Table 1 RADARSAT-2 SAR images acquired during the field campaign in Saskatoon (July 2008). Day (July 2008)

Flight direction

Beam mode

Incidence angle (°)

Polarization

19 19 22 23

D A A D

Fine quad-pol Scan narrow Scan narrow Fine

29–30.9 30–47 30–47 44.4–46.5

All HH, HV HH, HV HH, HV

The flight directions D and A refer respectively to descending and ascending overpasses.

3.2. Ground observations Coincident with the RADARSAT-2 satellite overpasses, field campaign measurements of soil surface roughness, moisture and texture as well as crop biophysical parameters (height and vegetation water content) were conducted over the wheat, lentil, pea, fallow, pasture, and canola fields. Soil surface roughness was measured with a 3-m profile of a pin meter. For each field, the roughness is computed by averaging the roughness parameters (the standard height and the correlation length) obtained from three measurement points sparsely distributed. Soil moisture was measured using the Hydra Probe II connected to a data logging device (Stevens Water Monitoring System, 2007). The accuracy of the Hydra Probe is +/− 0.03 water fraction by volume. For each sampled field, measurements were collected at 60 locations uniformly distributed over 4 transects. Finally, field mean soil moisture values were computed. Soil texture characterization was performed in the laboratory of the Department of Applied Geomatics (University of Sherbrooke) by the hydrometer method. The soils are loamy sand, sandy loam, sandy clay, clay loam and clay. The percentages of clay, sand, and loam over the fields, respectively, vary in the following range [15%-29%], [17%-50%], and [33%-61%]. The water content of samples of wheat, peas, canola, fallow and pasture collected from 0.50 × 0.50 m squares selected at random was determined by weighing before and after oven drying (wet weight– dry weight) to estimate the vegetation water content. Table 2 presents the collected data. 4. Methodology To achieve the soil moisture estimation over agricultural fields, a method is proposed, based on the combination of semi-empirical backscattering models of soil and vegetation with empirical relationships derived from multi-polarization RADARSAT-2 data. The schematic

Fig. 1. Location of the study area.

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Table 2 Summary of the field measurements collected in July 2008. Date

Crop type

No. of fields

Range of rms roughness (cm)

Range of correlation length (cm)

Range of soil moisture (% vol.)

Range of crop height (cm)

Range of crop water content (kg/m2)

19–24 July

Wheat Peas Lentil Fallow Pasture Canola

6 4 1 3 1 1

[1.48–2] [1.47–1.89] 1.74 [1.36–2.42] 1.87 1.81

[9–24] [10.7–31.2] 28.3 [13.8–39.8] 44.2 10

[9–30] [7–22] [14.4–21.4] [8–32] [19.5–25] [12.6–20]

[33–87] [44–54] 26.75 [11–16] 24 97

[1.5–3.3] [2.5–3.1] 1.98 – 0.54 5.10

diagram of the soil moisture retrieval algorithm is presented in Fig. 2. It consists of three steps: 1. Development of new empirical relationships to estimate crop height (h), soil surface roughness (s) and vegetation water content (WC) values for each field using multi-polarization SAR data, 2. Parameterization of the Water–Cloud model (Eq. (6)) to determine the parameters A and b for each crop type, 3. Inversion of soil moisture values (Ms) for each field.

4.1. Estimation of h, s and WC To assess the soil moisture (Ms) of agricultural fields from Eq. (6) and Eq. (1), a prior estimation of crop height (h), soil surface roughness (s) and vegetation water content (WC) is required. This is performed from empirical relationships based on multi-polarization RADARSAT-2 data. The depolarization ratio (χv), the co-polarized correlation coefficient (ρvvhh) and the ratio of the absolute value of the cross polarization to crop height (Λvh) were analyzed with respect to changes in soil surface roughness, crop height, soil moisture, vegetation water content, and incidence angle. The resulting empirical relationships for soil surface roughness, crop height and crop water content estimation are the principal original aspect of this study.

A

4.1.1. Co-polarized correlation coefficient The co-polarized correlation coefficient (ρvvhh) is a polarimetric parameter that represents the correlation between the co-polarized HH and VV channels (Lee et al., 1994). It is expressed as follows: j〈Shh Svv 〉j ffi ρvvhh = qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jShh j2 jSvv j2

ð7Þ

Fig. 3A presents the co-polarized correlation coefficient, derived at 30° from RADARSAT-2 data, as a function of crop height. It shows that ρvvhh is highly sensitive to crop height regardless to the crop type. At 30° incidence angle, the decreasing relationship observed between ρvvhh derived from RADARSAT-2 data and the measured crop height (10 b h (cm) b100) can be expressed by a logarithmic regression,
 ρvvhh;empirical;30 = −0:047 log ðhÞ + 1:02 R2 = 0:88

To understand the behaviour of ρvvhh with the changes in incidence angles, simulations of ξ = jSpq j2 and jShh Svv j are performed at 35° and 45° incidence angles using the cosinus model of the form ξ30° /cos φ(θ −30°) (Shi et al., 1994; Ulaby et al., 1982). The function cos φ(θ − 30°) represents the mean angular dependence of the backscattered power for a given polarization; φ is a parameter that depends on the dominant

B

C

Field data

SvvShh

ρvvhh =

Shh

2

Svv

2

0 0 χv ( dB ) = σ vh - σ vv

Λvh =

0 σ vh

h

h

Parameterization A, b

s WC

( dB / cm)

0 σ tot

0

σ soil

Water-Cloud model

Oh model

0 σ vol

Soil moisture Ms

Inversion of crops parameters

ð8Þ

Parameterization

Soil moisture Inversion

Fig. 2. Schematic diagram of the soil moisture inversion.

I. Gherboudj et al. / Remote Sensing of Environment 115 (2011) 33–43

This ratio has been found very sensitive to variations in the roughness of bare fields (Ulaby et al., 1986). Over agricultural fields, this sensitivity can be disturbed by the vegetation effect. Our datasets showed that the ratio is very sensitive to both soil surface roughness (in centimeters) and crop height (in centimeters). In order to represent these relationships, our fields were first grouped into three classes based on soil surface roughness (s = 1.5, 1.8, and 2.1 cm). The measured depolarization ratio (χv) at 30° versus crop height was then plotted (Fig. 4A). It was observed that χv increases with the crop height and decreases with the soil surface roughness regardless of crop type. 0 0 Indeed, for bare soils, σvv Nσvh . Over agricultural fields, as crop height 0 0 increases, σvh increases faster than σvv , thus leading to the tendency of χv to increase with crop height (Lin et al., 2009). In the following discussion, the effects of crop height, soil surface roughness, soil moisture, vegetation water content and incidence angle are analyzed in theoretical terms.

1

Measurements

Measured co-polatized correlation coefficients

R2-0.88

Best fit 0.9

0.8

0.7 0

20

40

60

80

100

120

4.1.2.1. Crop height and soil surface roughness. In order to demonstrate the theoretical relationship between the depolarization ratio (χv), crop height and soil surface roughness, simulations were performed using the Water–Cloud model (Eq. (6)) with the following input values: crop height (20 b h (cm)b 100), standard deviation of soil surface roughness

Crop height (cm)

B Simulated co-polarized correlation coefficients

1

θ=35° θ=45°

0.9

A 0.8

0.7

0.6

0.5 0

20

40

60

80

100

120

Crop height (cm) Fig. 3. Co-polarized correlation coefficients as function of crop height, (A) Measurements at 30° incidence angle, (B) Simulations at 35° and 45° incidence angles.

Measured HV-VV backscattering ratio (dB)

A

37

0 -2 -4 -6 -8 s=1.5 cm -10

s=1.8 cm s=2.1 cm

-12

Best fit s=1.5 cm Best fit s=1.8 cm

-14

Best fit s=2.1 cm -16 0


 ρvvhh;empirical;θ = −0:04 log ðhÞ−0:02θ + 1:64 R2 = 0:75

ð9Þ

20

40

60

80

100

120

Crop height (cm)

B Simulated HV-VV backscattering ratio (dB)

scattering mechanism and on sensor characteristics (Shi et al., 1994). Fig. 3B presents the simulations of the co-polarized correlation coefficients at 35° and 45° incidence angles vs the crop height. For a given crop height (h), Fig. 3B shows that the simulated ρvvhh decreases with an increase in the incidence angle. Indeed, an increase in the incidence angles, leads to an increase in the volume contribution into the total signal and thus to a decrease in the correlation between the HH and VV co-polarized channels. To account for this angular dependency on the relationship between ρvvhh vs h, Eq. (9) presents a generalized incidence angle regression with the following validity conditions applied to crop height and incidence angle θ, respectively: 10 b h (cm) b100, and 30° b θ b 45°.

0 -2 -4 -6 -8 -10 -12

s=0.9 cm

-14

s=1.5 cm s=2.1 cm

-16

4.1.2. Depolarization ratio The depolarization ratio (χv) is defined as VH to VV polarization expressed in dB (Ulaby et al. 1986): 0

0

χv = σvh ðdBÞ−σvv ðdBÞ

ð10Þ

0

20

40

60

80

100

120

Crop height (cm) Fig. 4. Depolarization ratio (χv) of different crop types as function of crop height for different soil surface roughness values at an incidence angle of 30°: (A) Measured χv, (B) Simulated χv using the Water–Cloud model (A = 0.0015 and b = 0.295 for VH and A = 0.0018 and b = 0.13 for VV; WC = 2.92 kg/m2 and Ms = 14% vol.

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(s = 0.9, 1.5, and 2.1 cm), vegetation water content WC= 2.92 kg/m2, soil moisture Ms = 14 (% vol.), A and b values of peas crop estimated at 30° incidence angle (see Table 4 in Section 4.2). Simulation results presented in Fig. 4B confirm the dependence of the depolarization ratio on both the crop height and soil surface roughness. A high sensitivity of χv to crop height and soil surface roughness is observed for short crops. In addition, the increasing and decreasing trends of χv respectively with increasing h and s values are in agreement with the measurements shown in Fig. 4A while the bias (less than 1 dB) observed between the theoretical and the measured χv values can be explained by a) the input parameters (A and b values corresponding to a given crop for which mean values of WC and h are used), and b) unresolved scattering mechanisms, namely the soil-vegetation interaction term, which is neglected in the Water–Cloud model. 4.1.2.2. Soil moisture. Fig. 5A shows the measured χv as function of crop height for different values of soil surface roughness and soil moisture measured over the fields (Ms is indicated beside each data point). It can be seen that the Ms measurements are greater than 15 (% vol.) with the exception of one value which is around 10 (% vol.). There is no effect of Ms values greater than 15 (% vol.) on the measured χv. To confirm this observation, simulations were performed using the Water–Cloud model

with the following input parameters: crop height h ranging from 10 to 100 cm, soil moisture = 10, 20 and 30 (% vol.), vegetation water content= 2.92 kg/m2, soil surface roughness = 1.9 cm and an incidence angle of 30°. Results presented in Fig. 5B show that the simulated χv is less sensitive to moderate to high Ms values (N 15% vol.). Indeed, while an increase in the soil moisture from 10 to 20 (% vol.) causes a decrease of 21% in χv, an increase in the soil moisture from 20 to 30 (% vol.) causes a decrease of 10% in χv (less than 1dB). 4.1.2.3. Vegetation water content. Fig. 6A is a plot of measured χv as function of crop height for different values of soil surface roughness and vegetation water content measured over the fields (WC is indicated beside each data point). It can be seen that there is no effect of WC on measured χv. To confirm the non-dependence of χv with WC, simulations were performed using the Water–Cloud model with the following input parameters: crop height ranging from 10 to 100 cm, soil moisture = 12 (% vol.), soil surface roughness = 1.9 cm, vegetation water content = 1.5, 2.5 and 5.1 kg/m² and an incidence angle θ = 30°. Results presented in Fig. 6B show that the simulated χv is insensitive to WC. In summary, the analyses conducted above using both experimental data and simulations demonstrate that crop height and soil

A 0

Measured HV-VV backscattering ratio (dB)

Measured HV-VV backscattering ratio (dB)

A

-2 18.5

-4 17.2 -6 9.3 -8

18.6

14.88 15.9

16.1

24.75

-10 -12

31

s=1.5 cm

-2 3.28

-4 2.88

5.12

2.08

3.15

-6 1.48 -8

1.55

2.52 0.54 1.98

-10 -12

s=1.5 cm

-14

s=1.8 cm s=2.1 cm

s=1.8 cm

-14

-16 0

s=2.1 cm -16

0

0

20

40

60

80

100

20

120

40

60

80

100

120

Crop height (cm)

Crop height (cm)

B

0

0

Simulated HV-VV backscattering ratio (dB)

Simulated HV-VV backscattering ratio (dB)

B

-2 -4 -6 -8 -10 -12

Ms=10% vol.

-14

Ms=20% vol.

0

20

40

60

80

100

-4 -6 -8 -10 -12

WC=1.5 kg/m2

-14

WC=2.5 kg/m2 WC=5.1 kg/m2

Ms=30% vol. -16

-2

120

Crop height (cm) Fig. 5. Depolarization ratio (χv) as a function of crop height at an incidence angle of 30°: (A) Measured χv for different values of soil surface roughness (values on graph are volumetric soil moisture measurements in %), (B) Simulated χv for different values of soil moisture using the Water–Cloud model (A = 0.0015 and b = 0.295 for VH and A = 0.0018 and b = 0.13 for VV) for s = 1.9 cm and WC = 2.92 kg/m2.

-16 0

20

40

60

80

100

120

Crop height (cm) Fig. 6. Depolarization ratio (χv) as a function of crop height at an incidence angle of 30°: (A) Measured χv for different values of soil surface roughness (values on graph are vegetation water content measurements in kg/m²), (B) Simulated χv for different values of vegetation water content using the Water–Cloud model (A = 0.0015 and b = 0.295 for VH and A = 0.0018 and b = 0.13 for VV) for s = 1.9 cm and Ms = 14% vol.

I. Gherboudj et al. / Remote Sensing of Environment 115 (2011) 33–43

surface roughness significantly affect the depolarization ratio (χv), in contrast to vegetation water content and moderate to high soil moisture values (N15% vol.). Based on Fig. 4, an empirical relationship between χv, h and s at an incidence angle of 30° can be established as shown in Eq. (11) and is valid under the following conditions: 10 b h (cm) b 100, Ms N 15 (% vol.), and 1.5 b s (cm) b 2.4, θ = 30°. 0:50

χv;empirical;30 ðdBÞ = 1:75s

0:66

log ðhÞ−10:58s


 2 R = 0:92

ð11Þ

4.1.2.4. Incidence angle. The effect of incidence angle on the depolarization ratio was considered from the perspective of the 0 0 general trend of σvh and σvv with changes in θ. Indeed, over vegetation cover, the decrease in σ0vh with increasing incidence angle is smaller 0 than the decrease in σvv (Ulaby and Dobson, 1989). The depolarization 0 0 ratio in dB (χv = σvh(dB) − σvv (dB)) therefore increases with incidence angle. To account for this angular dependency in the relationship between χv, h and s, Eq. (12) presents a generalised form of the empirical regression (Eq. (11)) obtained at θ = 30°. b2

χv;empirical;θ ðdBÞ = a1 ⁎sa2 log ðhÞ + b1 ⁎s


 2 R = 0:75

ð12Þ

where a1 a2 b1 b2

Table 3 β and α coefficients of Eq. (13) obtained for different values of vegetation water content of wheat and peas crops. WC (kg/m²)

Wheat β

α

β

Peas α

1.5 2.5 5.1

33.50 37.74 46.02

–0.150 –0.156 –0.166

44.59 45.07 46.37

–0.33 –0.30 –0.27

Using the Water–Cloud model, simulations of the cross polarized 0 backscattering coefficient (σvh ) were performed for wheat, and peas at 30° incidence angle with the following input values: crop height h varying from 10 to 200 cm, vegetation water content values of 1.5, 2.5, and 5.1 (kg/m²), soil moisture =14 (% vol.), and soil surface roughness =1.9 cm. For an empirical modeling, the absolute values of the simulated 0 backscattering coefficients (jσvh j) as a function of the crop height for different values of vegetation water content are presented in Fig. 7. An increasing and decreasing relationships are respectively observed 0 between jσvh j and the vegetation water content and the crop height. These relationships (Fig. 7) can be approximated to power-law function of the following form:

jσvh0 j = βhα

= −3:75θ + 3:67 = 1:44θ−0:25 = 18θ−19:94 = 0:75θ + 0:28

In Eq. (12), the empirical parameters ai and bi were estimated from three RADARSAT-2 images acquired at different incidence angles (30°, 33° and 45°) over agricultural fields with the following characteristics: 10 b h (cm) b 100, Ms N 15 (% vol.), 1.5 b s (cm) b 2.4. Once crop height has been determined from Eq. (9), Eq. (12) can be used to retrieve soil surface roughness (s) from a single RADARSAT-2 acquisition. 4.1.3. The ratio of the absolute value of cross polarization coefficient to crop height 0 Over vegetation covered soils, σvh is mainly dominated by the volume scattering (Ulaby et al., 1986) that depends on crop height, vegetation water content, crop type and structure.

35

Wheat (WC=2.5 kg/m2)

θ=30°

Peas (WC=5.1 kg/m2)

jσvh0 j = β′ WC κ hα

ð14Þ

0 Let us define Λvh as the ratio of jσvh j to the crop height h (cm),

Λvh =

jσvh0 ðdBÞj

ð15aÞ

h

ð15bÞ

Fig. 8 presents Λvh ratios computed from our RADARSAT-2 data at 30° and 44° incidence angles against the product of WC × h computed from field measurements. The behaviour of Λvh vs the product WC× h shows a non-dependence to the crop types and to the incidence angle (due to the weak angular dependence of σ0vh, Ulaby et al., 1986; Ulaby and Dobson, 1989). Therefore, considering Eq. (15b) and Fig. 8, the Λvh ratio can be expressed by the following empirical regression:

Peas (WC=2.5 kg/m2) 25

Table 3 presents the estimated values of the coefficients α and β for different values of vegetation water content of wheat and peas 0 crops. While the coefficient α drives the evolution of jσvh j as a function of the crop height, the coefficient β expresses the attenuation caused by the canopy. Therefore β varies with the vegetation water content WC (Table 3). This variation can be also expressed using a 0 power-law function (Table 3) and jσvh j (Eq. (13)) can be rewritten as a function of the crop height and the vegetation water content as follow,

Λvh = f ðWC × hÞ

Wheat (WC=1.5 kg/m2)

30

ð13Þ

Considering Eqs. (14)-(15a), Λvh can be given as function of the product WC × h

Wheat (WC=5.1 kg/m2)

Absolute value of the simulated HV backscattering coefficient (dB)

39

Peas (WC=1.5 kg/m2)

20

15

Λvh;empirical ðdBÞ = c1 ⁎ðWC×hÞc2 10

5 0

50

100

150

200

Crop height (cm) Fig. 7. Absolute value of the simulated HV backscattering coefficient by Water-Cloud model (A = 0.00025 and b = 0.35 for wheat, and A = 0.0015 and b = 0.295 for peas) as function of crop height at 30°.

ðR2 = 0:89Þ

ð16Þ

With c1 = 4.83 and c2 = -0.56; c1 and c2 are two empirical coefficients derived from the best match of Eq. (16) to the experimental data. They are obtained under the following conditions, closely related to our dataset: 0.55 b WC (kg/m2) b 5.10 and 10b h (cm)b 100. Once crop height (h) has been determined from Eq. (9), Eq. (16) can be used to estimate WC from RADARSAT-2 acquisition over agricultural fields satisfying the above-mentioned conditions on WC and h.

40

I. Gherboudj et al. / Remote Sensing of Environment 115 (2011) 33–43

Ratio of the absolute value of the cross polarization coefficient to crop height (dB/cm)

1,2

Table 4 presents the estimated A and b values for each crop type with respect to the polarization and the incidence angles of our images (Table 1). For wheat, parameter b was greater for VV polarization than for HH and VH polarizations. This is no doubt due to the vertical structure of this crop, which attenuates the radar signal in vertical polarization (VV) more than it does in HH and VH polarizations as noted by Ulaby et al. (1986). For the other crops, parameter b was weakly dependent on polarization. This is due mainly to the random distribution of the scattered elements within the vegetation medium. The estimated values of b are in agreement with several published results (Haboudane et al., 1996; Van De Griend and Wigneron, 2004; Wigneron et al., 1995).

θ=30° θ=45°

1

0.8

0.6

0.4

0.2

4.3. Inversion of soil moisture 0 0

100

200

300

400

500

WC x h Fig. 8. Ratio of the absolute value of the cross polarization coefficient to crop height as function of the product WC × h.

4.2. Water–Cloud model parameterization The parametrization of the Water–Cloud model consists into the estimation of the unknown parameters A and b for each crop type (wheat, peas, and lentils) and radar configuration (polarization, and incidence angle, and frequency) to allow good simulation of the total backscattering coefficient. The experimental data (vegetation water content, crop height, soil surface roughness and soil moisture) of (N) fields covered with the same crop type (Table 2) were used in the Water–Cloud model (Eq. (6)) to simulate the backscattering coefficients of fields covered with the same crop type. The values of A and b were then derived from a non-linear minimization process applied to the cost function F described as follows: N

F= ∑

i=1

 o 2 o σmeasured −σsimulated i

ð17Þ

where,

Table 4 Estimated values of A and b for mature crops. Crop type

Parameters

Wheat

A b bias rms error N° data A b bias rms error N° data A b bias rms error N° data

Lentils

5. Results 5.1. Retrieving the h, WC, s and Ms Using the multi-polarization information of RADARSAT-2 SAR images acquired on July 19, 2008, empirical relationships were developed to estimate soil surface roughness (s), crop height (h), and vegetation water content (WC) for each agricultural field. In Fig. 9A–C, the results were compared with the available ground measurements. Average relative errors (ARE) of 19%, 10% and 25.5% were obtained respectively for the retrieval of crop height, soil surface roughness and vegetation water content. They were computed using: ARE =

N Number of fields with the same crop type 0 σmeasured RADARSAT-2 measurements 0 σsimulated simulation values

Peas

Using the estimated A, b, h, and WC values, the volume backscattering 0 contribution, σvol , expressed by Eq. (2) and the two-way transmissivity of the vegetation layer (Eqs. (3) and (5)) can be simulated. They will be used to correct RADARSAT-2 backscattering coefficient from the vegetation effect and then using the estimated soil surface roughness to have access to soil moisture. The soil moisture retrieval is directly performed from HH and HV polarizations data and the simulations of the co-polarization ratio p and cross-polarization ratio q using the semi-empirical Oh model (2004) expressed by Eq. (1).

Unit

– kg/m2 dB dB – – kg/m2 dB dB – – kg/m2 dB dB –

30°

45°

HH

VV

VH

HH

HV

0.00095 0.335 0.18 0.90 3 0.0035 0.185 0.27 0.7 2 – – – – –

0.0008 0.47 0.075 1.32

0.00025 0.35 0.04 1.22

0.0002 0.31 0.10 1.97

0.0018 0.13 0.02 0.67

0.0015 0.295 0.31 0.19

– – – – –

– – – – –

0.0012 0.30 0.05 1.53 8 0.0025 0.11 0.22 0.52 6 0.00035 0.07 0.03 1.79 2

0.001 0.15 0.04 0.36 0.00032 0.075 0.005 1.7

1 M jmeasuredi −retrievedi j ∑ M i=1 measuredi

ð18Þ

where, M is the number of a given parameter (crop height, soil surface roughness or vegetation water content), The subscript i refers to the measured and retrieved parameters. In the literature research works using radar data can be found for the estimation of crop height, vegetation water content, and soil surface roughness. Most of them are crop specific (Baghdadi et al., 2009; Blaes and Defourny, 2003; De Roo et al., 2001; Engdahl et al., 2001) in contrast to the empirical relationships developed in this paper. For example, the heights of different crops were estimated from the coherence values derived from pairs of ERS SAR tandem acquisition (Blaes and Defourny, 2003; Engdahl et al., 2001; Srivastava et al., 2006). The best result was obtained for wheat (Blaes and Defourny, 2003) with a mean absolute error as low as 7 cm and a mean relative error of 22% (19% in the present paper). Over bare soil, Hajnsek et al. (2003) presented an L-band inversion method of soil surface roughness and soil moisture based on Cloude-Pottier decomposition parameters (H, α and A). Relative errors of 29%, about 3 times higher than our results were obtained for soil surface roughness. As for the vegetation water content, it is estimated in this study from a relationship (Eq. (16)) with slightly higher value of R2 (0.89) compared to De Roo et al. (2001). However, the 25.5% relative error obtained for the estimation of the vegetation water content can partly result from the error in crop height estimation (Eq. (16)).

I. Gherboudj et al. / Remote Sensing of Environment 115 (2011) 33–43

B

Bias=-0.94; RMSE=13.65; R 2=0.75

100

Measured surface roughness (cm)

Measured crop height (cm)

A

80

60

40

20

0

0

20

40

60

80

2.1

1.9 1.8 1.7 1.6 1.5

Retrieved crop height (cm)

D

Bias=0.01; RMSE=1.01; R 2=0.65

6

1.5

1.6

1.7

1.8

1.9

2

2.1

Retrieved surface roughness (cm)

5

Measured soil moisture (% vol.)

Measured vegetation water content (kg/m 2)

C

Bias=0.01; RMSE=0.22; R 2=0.15

2

1.4 1.4

100

41

4

3

2

1

Bias=2.41; RMSE=5.65; R 2=0.60

50

40

30

20

July 19

10

July 22 July 23

0

0

1

2

3

4

5

6

Retrieved vegetation water content (kg/m 2)

0

0

10

20

30

40

50

Retrieved soil moisture (% vol.)

Fig. 9. Comparison of retrieved and measured vegetation and soil parameters: (A) Crop height (cm), (B) Soil surface roughness (cm), (C) Vegetation water content (kg/m2) and (D) Soil moisture (% vol.).

For soil moisture estimation, the estimated values of h, s, and WC on July 19, 2008, were considered as constant for the entire acquisition period (July 19-23, 2008) of the RADARSAT-2 images. This assumption is justified since h, s, and WC vary slowly over short time periods. In Fig. 9D, the retrieved soil moisture values were compared with the ground measurements used for the parameterization of the Water–Cloud model. An average relative error of about 32% was obtained over the agricultural fields, compared to 19% obtained over bare soils (Hajnsek et al., 2003). Using L-band POLSAR data to estimate the soil moisture over agricultural fields, Hajnsek et al. (2009) obtained rmse values varying from 3 to 14%. In the present paper, the relative error of about 32% (rmse of 5.65%, Fig. 9D) can be explained by: 1) The propagation of the estimation errors of the crop height, vegetation water content and soil surface roughness into the soil moisture inversion algorithm. For example, for relatively dry vegetated soils, an error of 1 kg m− 2 in the estimation of vegetation water content can result in an error of 0.1 m3 m− 3 gravimetric moisture content (Bindlish and Barros, 2001). Similarly, the estimation error of the crop height or the soil surface roughness may also affect the soil moisture estimation. 2) The effect of soil texture on the backscattering coefficient was ignored in the Oh (2004) model. Considering the range of variation

of the measured soil texture (Section 3.2), the performance of the soil moisture inversion algorithm can be reduced as shown by Srivastava et al. (2009). 5.2. Validation of the methodology Validation of the soil moisture results is performed using an independent soil moisture dataset of 8 fields (wheat and peas) which was not used in the parameterization of the Water–Cloud model. This independent dataset consists of soil moisture measurements of 3 sampled fields collected during the field campaign and of measurements collected from in-situ network of soil moisture monitoring probes installed at different depths (5 cm, 20 cm and 50 cm). These probes are managed by Environment Canada (http://pages.usherbrooke.ca/ canexsm10/). In Fig. 10, the 5-cm soil moisture measurements of both probes and sampled fields, recorded at a time close to RADARSAT-2 overpasses, were compared to the estimated values. As presented on Fig. 10, the retrieved soil moisture values of the sampled fields are more accurate than that of Environment Canada (EC) network because they are more representative of the average condition of the entire field. Based on the results shown in Fig. 10, it is likely that some of the in situ monitoring locations are not representative of the field mean. The bias, rms error and R2 value of the sampled fields and EC network are

42

I. Gherboudj et al. / Remote Sensing of Environment 115 (2011) 33–43

EC network: bias=6.4; RMSE=6.6; R2=0.61 Sampled fields: bias=1.72; RMSE=5.9; R2=0.73

50

estimated over various crop fields with an average relative error of 32%. Better soil moisture estimation is expected with L-Band SAR data and by integrating the soil-vegetation interaction into the modeling of the backscattering coefficient.

EC network

Retrieved soil moisture (% vol.)

Sampled fields 40

Acknowledgments This study received funding from an NSERC strategic grant. The authors thank the Canadian Space Agency for providing the RADARSAT-2 images through the SOAR program and all the collaborators of Brenda Toth (Environment Canada, MSC Hydrometeorology and Arctic Lab) as well as Jon Belanger, Justin Adams, Lisa Courtney and Louis-Philippe Rousseau, who participated in ground data measurements. The authors also thank Mariette Lambert (laboratory supervisor) for her help during the laboratory experiments. Two anonymous reviewers provided helpful comments that contributed to improve the paper.

30

20

10

References 0

0

10

20

30

40

50

Measured soil moisture (% vol.) Fig. 10. Validation of soil moisture inversion results (% vol.) from RADARSAT-2 images using Environment Canada (EC) network measurements and sampled field measurements.

respectively (1.72; 6.4), (5.9; 6.6) and (0.73; 0.61). The rmse values are in the range obtained by Hajnsek et al. (2009) using a more efficient frequency (L-band) for soil moisture estimation over agricultural areas. The obtained average relative errors of the sampled fields and EC network are respectively 26% and 53%. 6. Conclusion In this paper, RADARSAT-2 linear polarization data and ground observations acquired simultaneously over various mature crop types were used in the semi-empirical Water–Cloud model to retrieve the soil moisture. To achieve the main objective of this study, empirical relationships were first proposed from RADARSAT-2 multi-polarization information. These relationships were used for the retrieval of crop height, vegetation water content and soil surface roughness, necessary for an easy estimation of soil moisture using the Water–Cloud model. We found that the co-polarized correlation coefficient (ρvvhh) was related to crop height with a determination coefficient R2 = 0.88 at an incidence angle of 30°. A relationship which accounts for the angular dependency between the depolarization ratio (χv), soil surface roughness, crop height was established with a determination coefficient R2 = 0.75. The obtained relationships were then used for the retrieval of crop height and soil surface roughness over each agricultural field. The ratio of the absolute value of the cross polarization to the crop height (Λvh) was related to the product of the crop height and vegetation water content (WC× h) with a determination coefficient R2 = 0.89. This ratio (Λvh) was used to retrieve the vegetation water content. The main advantage of the paper is the possibility to successively apply the 3 relationships to infer h, s and WC from a single multipolarization acquisition of radar data. The results could be subsequently used for the mapping of soil moisture over agricultural fields. The originality of this study is that the proposed empirical relationships are independent of crop type, contrary to those found in the literature. They allow us to estimate over various crop fields, soil surface roughness, crop height and vegetation water content with average relative errors of respectively 19%, 10% and 25.5%. Soil moisture is

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